How to Solve the Hardest Logic Puzzle Ever


Brian Gallagher in Nautilus:

The Hardest Logic Puzzle Ever goes like this:

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for “yes” and “no” are “da” and “ja,” in some order. You do not know which word means which.

Always up for a challenge, I sat down on my couch, pen and paper in hand, confident I could conquer the puzzle in two hours tops. It seemed to me that all I had to do was start by coming up with three questions at once and then work out their consequences. I asked A, for example, whether B was True; asked B whether A was True; and asked C whether he was True. Hours later, having asked the gods every yes and no question I could think of, I understood how the puzzle got its name. Clearly my questions weren’t compelling the gods to answer the way I wanted them to.

Frustrated, I went in search of enlightenment. The master atop the mountain turned out to be Boolos, who solved the puzzle in 1996. How he did it turns out to be one of the best lessons in logic and truth I have ever received. If you’d like to give the puzzle a try yourself, you can stop reading here. Good luck! If you succeed, you have my congrats. But if you don’t, come on back and you can go over Boolos’ solution with me below.

More here.